FORTUNE — The social media giant Facebook is seeking a license from Ireland’s central bank that would allow it to become an e-money institution able to issue its own online currency similar to Bitcoin, according to sources familiar with the deal. The news was first reported by The Irish Times and others earlier this month.

Facebook’s e-money — which might receive regulatory approval as early as this month — would be valid across Europe and allow its users to store and exchange digital currency over the social network. Facebook (FB) has also entered into discussions with a number of European companies that facilitate international remittances of money over the web.

“Its focus on mobile money transfers makes sense,” says Eden Zoller, a London-based analyst with technology research firm Ovum. “These applications are gaining good traction with consumers, particularly in emerging markets where Facebook has ambitions to be the prime platform from which people access and interact with Internet services.”

If Facebook succeeds in obtaining an e-money license for Europe it will be joining other non-banking companies — including Google (GOOG), Vodafone (VOD), T-Mobile (TMUS), and Sprint (S) — who are competing head-to-head with traditional banks by offering mobile and web-based financial services.

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This burgeoning trend promises to radically reshape the global banking industry by knocking down barriers to competition and bringing financial inclusion to the world’s unbanked masses in developing countries from Haiti and Afghanistan to Kenya and Zimbabwe.

The Bank of Facebook? It’s a radical idea, but it could boost the Menlo Park, Calif.-based company’s revenue and keep it relevant to a new generation of mobile users who have eschewed its status updates and candid photos. But a move into e-money and financial services would mark a major strategic shift for a company that today generates the bulk of its revenue and profit from advertising.

But there remains a huge untapped market for banking services, including the exchange of money between family and friends living in different cities, and international money transfers between family in developed and developing countries. For this reason, e-money makes sense: Facebook has some 200 million members in Asia, for example. (About half of those are in India, which is Facebook’s single largest market outside the U.S.)

Google has already obtained an e-money license in Europe, and last year it introduced a new version of Google Wallet for Android phones, making it possible to send money to anyone in the U.S. who has an e-mail address.

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The U.S. wireless carriers T-Mobile and Sprint have in the last 12 months launched mobile money services that cater to the 68 million Americans without a bank account or debit card. These services use a smartphone app that makes it possible to conduct a variety of transactions, including check deposit, retail purchases, and bill payment.

U.K.-based Vodafone — which, like Google, has an e-money license for Europe — is perhaps the biggest trailblazer among non-banking companies when it comes to offering banking services, and is a driving force behind Kenya’s M-Pesa, the world’s most successful mobile money wallet.

But Facebook may be in for an uphill battle when it comes to convincing users in developed and developing countries that its proposed online currency is a safe bet.

“Facebook will have its work cut out, and the biggest challenge will be consumer trust,” Zoller says, adding the firm’s research indicates just 1% of people trust social networks like Facebook to handle m-payments, compared to 43% for banks 13% for credit card companies.

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And the ongoing issues with Bitcoin — scandal, fraud, volatility — hurt electronic currency’s reputation and serve as a hurdle for Facebook, which has had its own issues dealing in e-commerce. “The Facebook Credits virtual currency got nowhere and was wound down last year,” Zoller says, “while the main m-commerce offering in place today, Facebook Gifts, has so far received a muted response from consumers.”